Abstract

Phase-locked second and third harmonic generation in the opaque region of a GaAs wafer is experimentally observed and analyzed both in transmission and reflection. These harmonic components, which are generated close to the surface, can propagate through an opaque material as long as the pump is tuned to a region of transparency or semitransparency and correspond to the inhomogeneous solutions of Maxwell’s equations with nonlinear polarization sources. We show that measurement of the angular and polarization dependence of the observed harmonic components allows one to infer the different nonlinear mechanisms that trigger these processes, including not only the bulk nonlinearity but also the surface and magnetic Lorentz contributions, which usually are either hidden by the bulk contributions or assumed to be negligible. The experimental results are compared with a detailed numerical model that takes into account these different effects, including for the first time combined linear and nonlinear material dispersions in a nonlinear Lorentz oscillator model of the bulk nonlinearities. Our results suggest that the intensity of the second harmonic signal generated by the surface can be more intense than the signal generated by the bulk. These findings have significant repercussions and are consequential in nanoscale systems, which are usually investigated using only dispersionless bulk nonlinearities, with near-complete disregard of surface and magnetic contributions and their microscopic origins.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
    [Crossref]
  2. N. Bloembergen, R. K. Chang, and C. H. Lee, “Second-Harmonic Generation of Light in Reflection from Media with Inversion Symmetry,” Phys. Rev. Lett. 16(22), 986–989 (1966).
    [Crossref]
  3. L. D. Noordam, H. J. Bakker, M. P. de Boer, and H. B. van Linden van den Heuvell, “Second-harmonic generation of femtosecond pulses: observation of phase-mismatch effects,” Opt. Lett. 15(24), 1464–1466 (1990).
    [Crossref]
  4. V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
    [Crossref]
  5. M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
    [Crossref]
  6. V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
    [Crossref]
  7. V. Roppo, J. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98(11), 111105 (2011).
    [Crossref]
  8. V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity,” Opt. Lett. 36(10), 1809 (2011).
    [Crossref]
  9. M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
    [Crossref]
  10. M. Scalora, M. Vincenti, D. de Ceglia, N. Akozbek, V. Roppo, M. Bloemer, and J. W. Haus, “Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths,” Phys. Rev. A 85(5), 053809 (2012).
    [Crossref]
  11. M. Scalora, M. Vincenti, D. de Ceglia, C. M. Cojocaru, and J. W. Haus, “Nonlinear Duffing oscillator model for third harmonic generation,” J. Opt. Soc. Am. B 32(10), 2129–2138 (2015).
    [Crossref]
  12. M. Scalora, J. Trull, C. Cojocaru, M. A. Vincenti, L. Carletti, D. de Ceglia, N. Akozbek, and C. De Angelis, “Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths,” arXiv:1905.04516 (2019)
  13. R. W. Boyd, Nonlinear Optics (Academic, 2003).
  14. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985)
  15. J. Qi, Nonlinear Optical Spectroscopy of Gallium Arsenide Interfaces (University of Pennsylvania, 1995).
  16. M. Rebiena, W. Henrion, M. Hong, J. P. Mannaerts, and M. Fleischer, “Optical properties of gallium oxide thin films,” Appl. Phys. Lett. 81(2), 250–252 (2002).
    [Crossref]

2015 (1)

2012 (1)

M. Scalora, M. Vincenti, D. de Ceglia, N. Akozbek, V. Roppo, M. Bloemer, and J. W. Haus, “Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths,” Phys. Rev. A 85(5), 053809 (2012).
[Crossref]

2011 (2)

V. Roppo, J. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98(11), 111105 (2011).
[Crossref]

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity,” Opt. Lett. 36(10), 1809 (2011).
[Crossref]

2010 (1)

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

2009 (1)

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

2008 (1)

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

2007 (1)

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

2002 (1)

M. Rebiena, W. Henrion, M. Hong, J. P. Mannaerts, and M. Fleischer, “Optical properties of gallium oxide thin films,” Appl. Phys. Lett. 81(2), 250–252 (2002).
[Crossref]

1990 (1)

1966 (1)

N. Bloembergen, R. K. Chang, and C. H. Lee, “Second-Harmonic Generation of Light in Reflection from Media with Inversion Symmetry,” Phys. Rev. Lett. 16(22), 986–989 (1966).
[Crossref]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Akozbek, N.

M. Scalora, M. Vincenti, D. de Ceglia, N. Akozbek, V. Roppo, M. Bloemer, and J. W. Haus, “Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths,” Phys. Rev. A 85(5), 053809 (2012).
[Crossref]

V. Roppo, J. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98(11), 111105 (2011).
[Crossref]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

M. Scalora, J. Trull, C. Cojocaru, M. A. Vincenti, L. Carletti, D. de Ceglia, N. Akozbek, and C. De Angelis, “Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths,” arXiv:1905.04516 (2019)

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Bakker, H. J.

Bertolotti, M.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

Bloembergen, N.

N. Bloembergen, R. K. Chang, and C. H. Lee, “Second-Harmonic Generation of Light in Reflection from Media with Inversion Symmetry,” Phys. Rev. Lett. 16(22), 986–989 (1966).
[Crossref]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Bloemer, M.

M. Scalora, M. Vincenti, D. de Ceglia, N. Akozbek, V. Roppo, M. Bloemer, and J. W. Haus, “Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths,” Phys. Rev. A 85(5), 053809 (2012).
[Crossref]

Bloemer, M. J.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Carletti, L.

M. Scalora, J. Trull, C. Cojocaru, M. A. Vincenti, L. Carletti, D. de Ceglia, N. Akozbek, and C. De Angelis, “Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths,” arXiv:1905.04516 (2019)

Centini, M.

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

Chang, R. K.

N. Bloembergen, R. K. Chang, and C. H. Lee, “Second-Harmonic Generation of Light in Reflection from Media with Inversion Symmetry,” Phys. Rev. Lett. 16(22), 986–989 (1966).
[Crossref]

Cojocaru, C.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity,” Opt. Lett. 36(10), 1809 (2011).
[Crossref]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

M. Scalora, J. Trull, C. Cojocaru, M. A. Vincenti, L. Carletti, D. de Ceglia, N. Akozbek, and C. De Angelis, “Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths,” arXiv:1905.04516 (2019)

Cojocaru, C. M.

D’Aguanno, G.

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

De Angelis, C.

M. Scalora, J. Trull, C. Cojocaru, M. A. Vincenti, L. Carletti, D. de Ceglia, N. Akozbek, and C. De Angelis, “Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths,” arXiv:1905.04516 (2019)

de Boer, M. P.

de Ceglia, D.

M. Scalora, M. Vincenti, D. de Ceglia, C. M. Cojocaru, and J. W. Haus, “Nonlinear Duffing oscillator model for third harmonic generation,” J. Opt. Soc. Am. B 32(10), 2129–2138 (2015).
[Crossref]

M. Scalora, M. Vincenti, D. de Ceglia, N. Akozbek, V. Roppo, M. Bloemer, and J. W. Haus, “Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths,” Phys. Rev. A 85(5), 053809 (2012).
[Crossref]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

M. Scalora, J. Trull, C. Cojocaru, M. A. Vincenti, L. Carletti, D. de Ceglia, N. Akozbek, and C. De Angelis, “Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths,” arXiv:1905.04516 (2019)

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Fazio, E.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

Fleischer, M.

M. Rebiena, W. Henrion, M. Hong, J. P. Mannaerts, and M. Fleischer, “Optical properties of gallium oxide thin films,” Appl. Phys. Lett. 81(2), 250–252 (2002).
[Crossref]

Foreman, J.

V. Roppo, J. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98(11), 111105 (2011).
[Crossref]

Foreman, J. V.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

Halioua, Y.

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

Haus, J. W.

M. Scalora, M. Vincenti, D. de Ceglia, C. M. Cojocaru, and J. W. Haus, “Nonlinear Duffing oscillator model for third harmonic generation,” J. Opt. Soc. Am. B 32(10), 2129–2138 (2015).
[Crossref]

M. Scalora, M. Vincenti, D. de Ceglia, N. Akozbek, V. Roppo, M. Bloemer, and J. W. Haus, “Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths,” Phys. Rev. A 85(5), 053809 (2012).
[Crossref]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

Henrion, W.

M. Rebiena, W. Henrion, M. Hong, J. P. Mannaerts, and M. Fleischer, “Optical properties of gallium oxide thin films,” Appl. Phys. Lett. 81(2), 250–252 (2002).
[Crossref]

Hong, M.

M. Rebiena, W. Henrion, M. Hong, J. P. Mannaerts, and M. Fleischer, “Optical properties of gallium oxide thin films,” Appl. Phys. Lett. 81(2), 250–252 (2002).
[Crossref]

Kandidov, V. P.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

Kosareva, O. G.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

Lee, C. H.

N. Bloembergen, R. K. Chang, and C. H. Lee, “Second-Harmonic Generation of Light in Reflection from Media with Inversion Symmetry,” Phys. Rev. Lett. 16(22), 986–989 (1966).
[Crossref]

Mannaerts, J. P.

M. Rebiena, W. Henrion, M. Hong, J. P. Mannaerts, and M. Fleischer, “Optical properties of gallium oxide thin films,” Appl. Phys. Lett. 81(2), 250–252 (2002).
[Crossref]

Noordam, L. D.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985)

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Pettazzi, F.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

Qi, J.

J. Qi, Nonlinear Optical Spectroscopy of Gallium Arsenide Interfaces (University of Pennsylvania, 1995).

Raineri, F.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity,” Opt. Lett. 36(10), 1809 (2011).
[Crossref]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

Raj, R.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity,” Opt. Lett. 36(10), 1809 (2011).
[Crossref]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

Rebiena, M.

M. Rebiena, W. Henrion, M. Hong, J. P. Mannaerts, and M. Fleischer, “Optical properties of gallium oxide thin films,” Appl. Phys. Lett. 81(2), 250–252 (2002).
[Crossref]

Roppo, V.

M. Scalora, M. Vincenti, D. de Ceglia, N. Akozbek, V. Roppo, M. Bloemer, and J. W. Haus, “Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths,” Phys. Rev. A 85(5), 053809 (2012).
[Crossref]

V. Roppo, J. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98(11), 111105 (2011).
[Crossref]

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity,” Opt. Lett. 36(10), 1809 (2011).
[Crossref]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

Sagnes, I.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity,” Opt. Lett. 36(10), 1809 (2011).
[Crossref]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

Scalora, M.

M. Scalora, M. Vincenti, D. de Ceglia, C. M. Cojocaru, and J. W. Haus, “Nonlinear Duffing oscillator model for third harmonic generation,” J. Opt. Soc. Am. B 32(10), 2129–2138 (2015).
[Crossref]

M. Scalora, M. Vincenti, D. de Ceglia, N. Akozbek, V. Roppo, M. Bloemer, and J. W. Haus, “Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths,” Phys. Rev. A 85(5), 053809 (2012).
[Crossref]

V. Roppo, J. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98(11), 111105 (2011).
[Crossref]

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity,” Opt. Lett. 36(10), 1809 (2011).
[Crossref]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

M. Scalora, J. Trull, C. Cojocaru, M. A. Vincenti, L. Carletti, D. de Ceglia, N. Akozbek, and C. De Angelis, “Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths,” arXiv:1905.04516 (2019)

Sibilia, C.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

Trull, J.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity,” Opt. Lett. 36(10), 1809 (2011).
[Crossref]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

M. Scalora, J. Trull, C. Cojocaru, M. A. Vincenti, L. Carletti, D. de Ceglia, N. Akozbek, and C. De Angelis, “Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths,” arXiv:1905.04516 (2019)

van Linden van den Heuvell, H. B.

Vilaseca, R.

V. Roppo, F. Raineri, R. Raj, I. Sagnes, J. Trull, R. Vilaseca, M. Scalora, and C. Cojocaru, “Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity,” Opt. Lett. 36(10), 1809 (2011).
[Crossref]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

Vincenti, M.

M. Scalora, M. Vincenti, D. de Ceglia, C. M. Cojocaru, and J. W. Haus, “Nonlinear Duffing oscillator model for third harmonic generation,” J. Opt. Soc. Am. B 32(10), 2129–2138 (2015).
[Crossref]

M. Scalora, M. Vincenti, D. de Ceglia, N. Akozbek, V. Roppo, M. Bloemer, and J. W. Haus, “Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths,” Phys. Rev. A 85(5), 053809 (2012).
[Crossref]

Vincenti, M. A.

V. Roppo, J. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98(11), 111105 (2011).
[Crossref]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

M. Scalora, J. Trull, C. Cojocaru, M. A. Vincenti, L. Carletti, D. de Ceglia, N. Akozbek, and C. De Angelis, “Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths,” arXiv:1905.04516 (2019)

Appl. Phys. Lett. (2)

V. Roppo, J. Foreman, N. Akozbek, M. A. Vincenti, and M. Scalora, “Third harmonic generation at 223 nm in the metallic regime of GaP,” Appl. Phys. Lett. 98(11), 111105 (2011).
[Crossref]

M. Rebiena, W. Henrion, M. Hong, J. P. Mannaerts, and M. Fleischer, “Optical properties of gallium oxide thin films,” Appl. Phys. Lett. 81(2), 250–252 (2002).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Phys. Rev. A (4)

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, “Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media,” Phys. Rev. A 76(3), 033829 (2007).
[Crossref]

M. Scalora, M. A. Vincenti, D. de Ceglia, V. Roppo, M. Centini, N. Akozbek, and M. J. Bloemer, “Second- and third-harmonic generation in metal-based structures,” Phys. Rev. A 82(4), 043828 (2010).
[Crossref]

M. Scalora, M. Vincenti, D. de Ceglia, N. Akozbek, V. Roppo, M. Bloemer, and J. W. Haus, “Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths,” Phys. Rev. A 85(5), 053809 (2012).
[Crossref]

V. Roppo, C. Cojocaru, F. Raineri, G. D’Aguanno, J. Trull, Y. Halioua, R. Raj, I. Sagnes, R. Vilaseca, and M. Scalora, “Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities,” Phys. Rev. A 80(4), 043834 (2009).
[Crossref]

Phys. Rev. Lett. (2)

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, “Inhibition of Linear Absorption in Opaque Materials Using Phase-Locked Harmonic Generation,” Phys. Rev. Lett. 101(11), 113905 (2008).
[Crossref]

N. Bloembergen, R. K. Chang, and C. H. Lee, “Second-Harmonic Generation of Light in Reflection from Media with Inversion Symmetry,” Phys. Rev. Lett. 16(22), 986–989 (1966).
[Crossref]

Other (4)

M. Scalora, J. Trull, C. Cojocaru, M. A. Vincenti, L. Carletti, D. de Ceglia, N. Akozbek, and C. De Angelis, “Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths,” arXiv:1905.04516 (2019)

R. W. Boyd, Nonlinear Optics (Academic, 2003).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985)

J. Qi, Nonlinear Optical Spectroscopy of Gallium Arsenide Interfaces (University of Pennsylvania, 1995).

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Figures (7)

Fig. 1.
Fig. 1. Real (blue) and imaginary (red) part of the permittivity of GaAs.
Fig. 2.
Fig. 2. Predicted surface-and bulk-generated SH transmission and reflection angular dependence as a function of incident pump polarization. (a) Schematic representation of the GaAs sample showing the crystallographic axes and the TM and TE polarizations. A TM-polarized pump triggers a bulk-generated TE-polarized SH signal (b) and a surface-generated TM-polarized signal (d), as outlined in the text. A TE-polarized pump (c) is responsible for a TM-polarized SH signal, arising mostly from the magnetic Lorentz nonlinearity.
Fig. 3.
Fig. 3. Predicted THG for TM- (blue, dashed curve, open circle) and TE-polarized (red, solid curve, open squares) pumps.
Fig. 4.
Fig. 4. Setup for measuring SH and TH signals. The encircled area is mounted on a rotating stage so it can be used for transmission and reflection measurements.
Fig. 5.
Fig. 5. Calculated (red, solid curves with open squares) and measured (blue, dashed curves with open circles) SH transmission efficiencies as a function of the angle of incidence and pump polarization. The surface generated components [(a) and (c)] agree well with our measurements in both maximum amplitude and shape if the electron’s effective mass is chosen to be m*=0.0025me. The bulk-generated SH efficiency also agrees well with the experiment in both maximum amplitude and shape if the coefficient α corresponds to a χ(2) ∼ 20 - 40pm/V. The discrepancies between theory and experiment in (c) at large angles may in part be due to interference effects. The simulations are carried out for a 10µm-thick etalon and pulses a few tens of fs in duration. The experiment is performed using ps pulses and 500µm-thick substrate.
Fig. 6.
Fig. 6. Calculated (red, solid curves with open squares) and measured (blue, dashed curves with open circles) reflected SH efficiencies as a function of the angle of incidence and pump polarization. All the experimental and simulation parameters are the same as in Fig. 5.
Fig. 7.
Fig. 7. Calculated (red, solid curves, open squares) and measured (blue, dashed curves, open circles) for TM-(a) and TE-polarized (b) TH efficiencies as functions of the angle of incidence.

Equations (5)

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( P x N L ( 2 ) P y N L ( 2 ) P z N L ( 2 ) ) = ( ( α x , y , z + α x , z , y ) P z P y ( α y , x , z + α y , z , x ) P z P x ( α z , x , y + α z , y , x ) P y P x ) = α ( P z P y P z P P y P x ) ,
( P x N L ( 3 ) P y N L ( 3 ) P z N L ( 3 ) ) = β ( ( P x 2 + P y 2 + P z 2 ) P x ( P x 2 + P y 2 + P z 2 ) P y ( P x 2 + P y 2 + P z 2 ) P z ) .
P ¨ b 1 + γ b 1 P ˙ b 1 + ω 01 2 P b 1 + α 1 P b 1 P b 1 β 1 ( P b 1 P b 1 ) P b 1 = n 0 b 1 e 2 m b 1 E + e m b 1 c P ˙ b 1 × H ,
E = ( x ^ ( E T E x ^ ω ( r , t ) e i ( k r ω t ) + E T E x ^ 2 ω ( r , t ) e 2 i ( k r ω t ) + E T E x ^ 3 ω ( r , t ) e 3 i ( k r ω t ) + c . c ) y ^ ( E T M y ^ ω ( r , t ) e i ( k r ω t ) + E T M y ^ 2 ω ( r , t ) e 2 i ( k r ω t ) + E T M y ^ 3 ω ( r , t ) e 3 i ( k r ω t ) + c . c ) z ^ ( E T M z ^ ω ( r , t ) e i ( k r ω t ) + E T M y ^ 2 ω ( r , t ) e 2 i ( k r ω t ) + E T M z ^ 3 ω ( r , t ) e 3 i ( k r ω t ) + c . c ) ) ,
P ¨ b 1 + γ b 1 P ˙ b 1 + ω 01 2 P b 1 + P b 1 ( N L ) = n 0 b 1 e 2 m b 1 E + e m b 1 ( P b 1 ) E + e m b 1 c P ˙ b 1 × H + ,

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